Question

The Digital Electronic Quotation System (DEQS) Corporation pays no cash dividends currently and is not expected to for the next five years. Its latest EPS was $19.50, all of which was reinvested in the company. The firm’s expected ROE for the next five years is 15% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting in year 6, the firm’s ROE on new investments is expected to fall to 10%, and the company is expected to start paying out 50% of its earnings in cash dividends, which it will continue to do forever after. DEQS’s market capitalization rate is 26% per year.

a. What is your estimate of DEQS’s intrinsic value per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Intrinsic Value? $____

b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its price over the next year? (Round your dollar value to 2 decimal places.)

Price will --------- by --------% per year until year 6

Because there is ----- , the entire return must be in --------.

Price in one year?

c. What do you expect to happen to price in the following year? (Round your dollar value to 2 decimal places.)

Price in 2 years?---

d. What is your estimate of DEQS’s intrinsic value per share if you expected DEQS to pay out only 30% of earnings starting in year 6? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Intrinsic value?--------

Answer 1

(a) Current time is assumed to be t=0, The firm possesses an ROE of 15 % for the first five years during which period it reinvests all of its earnings, thereby posting a retention ratio of 1.

Hence, Growth Rate for the first 5 years = ROE x Retention Ratio = 15 x 1 = 15 %

Current EPS = $ 19.5 = E0

Expected Earnings :

E1 = 19.5 x 1.15 = $ 22.425

E2 = 22.425 x 1.15 = $ 25.78888

E3 = 25.7888 x 1.15 = $ 29.6571

E4 = 29.6571 x 1.15 = $ 34.1056

E5 = 34.1056 x 1.15 = $ 39.2215

At the end of Year 5, the firm's ROE grows down to 10% and it starts paying out 50% of earnings as dividends. Therefore, Retention Ratio at the end of Year 5 is 50%

Growth Rate for Year 6 = New ROE x New Retention Ratio = 10 x 0.5 = 5 %

Earnings at the end of year 6 = E6 = 1.05 x 39.2215 = $ 41.1825

Dividend Paid at the end of Year 5 = D5 = 39.2215 x 0.5 = $ 19.6107

Dividend Paid at the end of Year 6 = D6 = 19.6107 x 1.05 = $ 20.5913

Market Capitalization Rate = r= 26 %

Horizon Value of Perpetual Dividends at the end of Year 5 = H = D6 / (r - Perpetual Growth Rate) = 20.5913 / (0.26 - 0.05) = $ 98.0537

Intrinsic Price per Share = D5 / (1.26)^(5) + H / (1.26)^(5) = 19.6107 / (1.26)^(5) + 98.0537 / (1.26)^(5) = $ 37.0504 ~ $ 37.05

(b) Price will increase by the initial growth rate of 15% for five years until year 6. As there is no dividend, the entire return will be in the form of capital gains (price growth).

Price after 1 year = 37.0504 x 1.15 = $ 42.6079

(c) Price after 2 years = 42.6079 x 1.15 = $ 48.9991

(d) If DEQS pays out only 30% of earnings as dividends, then D5 = 0.3 x 39.2215 = $ 11.7664

Retention Ratio = 1-0.3 = 0.7

Growth Rate = 0.7 x 10 = 7 %

Dividend at the end of Year 6 = 11.7664 x 1.07 = $ 12.5901

Horizon Value of Perpetual Dividends at the end of Year 5 = 12.5901 / (0.26 - 0.07) = $ 66.2636

Intrinsic Price Per Share = 11.7664 / (1.26)^(5) + 66.2636 / (1.26)^(5) = $ 24.5702 ~ $ 24.57